For #1, I think we can say it in the following context:
1. A asks B: "Have you eaten smoked chicken claws when you lived in China?"
Then B can respond: "Yes. I have eaten smoked chicken claws since I lived in China."
Or B can respond: "No. I have eaten smoked chicken claws since I lived in China."
I think #1 can have two interpretations:
1) Assuming I lived in China for 180 days. I may have begun to eat smoked chicken claws on day 2. And I have eaten them from then up until now.
Day1.....Day2(ate)....Day3.......(ate).................Day180(I left China).......(ate).......Now(still eat)
2)It can also mean "I didn't start to eat smoked chicken claws until I left China". In this case, it is identical to "I have eaten smoked chicken claws since l left China".
Day1.............................(not ate).......................Day180(I left China).......(ate).......Now(still eat)